β: This English translation is in beta — the Traditional-Chinese original is the authoritative version.

Claims Cross-Reference

Every key teaching claim on this site is numbered C1–C13, each annotated with: which paper it comes from, how high the confidence is, whether it needs manual comparison against the PDF (Verify?), and which pages use it. Data comes from extracted/extracted_claims.json.

How to use this page: when writing a page or reviewing, first find which C-number a conclusion belongs to, then trace it back to the source paper and confidence level. Confidence has three levels: high (read from text) / high (equation verified) / medium. A ⚠️ in Verify? means manual_verification_needed = true — the constants or exact form still need manual comparison against the original PDF.

C1–C13 at a glance

Claim	Source Paper	Confidence	Verify?	Used on
C1 All oscillators are LTV, not LTI, with respect to noise: the same impulse injected at different instants of the period produces different phase shifts.	[P1] (paper_001) Sec. III	high (read from text)	No	lti_vs_ltv, isf_definition, lab_04
C2 Amplitude perturbations are pulled back to the limit cycle (stable oscillation requires a restoring mechanism), but phase perturbations persist and accumulate.	[P1] Sec. III-A; [P4] (APF/decay function)	high	No	oscillator_phase, phase_vs_amplitude_noise, impulse_to_phase_shift
C3 Phase noise $\propto\Gamma_{rms}^2/q_{max}^2$: increase the signal charge swing $q_{max}$ and lower the rms ISF to reduce $1/f^2$ phase noise.	[P1] Eq.(21)	high (equation verified)	No	white_noise_to_phase_noise, rms_isf, lab_06, lc_vs_ring
C4 $1/f$ device noise upconverts to close-in $1/f^3$ only through the ISF DC term $c_0$; rise/fall symmetry (small $c_0$) → low $1/f^3$.	[P1] Eqs (23),(24); [P2] symmetry section and Fig. 17	high	No	flicker_noise_upconversion, fourier_series_of_isf, symmetry, lab_07
C5 The $1/f^3$ corner is not the device $1/f$ corner: $\Delta\omega_{1/f^3}=\omega_{1/f}\,c_0^2/(2\Gamma_{rms}^2)$, so symmetry can push it below the device corner.	[P1] Eq.(24)	high (equation verified)	No	flicker_noise_upconversion, symmetry, equation_index
C6 A free-running oscillator's accumulated jitter grows as the square root of the measurement interval, $\sigma_{\Delta t}=\kappa\sqrt{\Delta t}$ — the random-walk signature of having no absolute time reference.	[P2] (paper_002) Eq.(8), p.792	high	No	psd_phase_noise_jitter, lab_03, serdes_clocking_connection
C7 At fixed center frequency and power dissipation, a single-ended ring's phase noise/jitter is essentially independent of the number of stages $N$.	[P2] Sec. V, Eq.(23)/(25), p.796	high (equation verified) ($N$-independence verified; only the FOM prefactor $8/(3\eta)$ is a detail)	No	lc_vs_ring, lab_03
C8 A single-ended ring's rms ISF scales roughly as $\Gamma_{rms}\propto N^{-3/2}$.	[P2] Eq.(16), p.794	high (equation verified)	No	rms_isf, lc_vs_ring, lab_03
C9 The ISF framework subsumes prior phase-noise models (e.g. Leeson) as special cases, and naturally accommodates cyclostationary noise via the effective ISF $\Gamma_{eff}=\Gamma\cdot\alpha$.	[P1] Abstract and cyclostationary section	high	No	effective_isf, paper_summary_table, equation_index
C10 The same ISF that determines phase noise also determines injection locking/pulling; a single first-order (generalized Adler) equation predicts lock range, locked phase, and stability.	[P3] (Hong Part I, 2019) Eq.(30), p.2113 / Eq.(35), p.2114	high (equation verified)	No	paper_003_injection_locking_part1, equation_index
C11 Amplitude effects under injection are described by the APF (amplitude perturbation function, the amplitude analogue of the ISF, units $\mathrm{A^{-1}}$); in an ideal LC the ISF and APF are orthogonal.	[P4] (Hong Part II, 2019) Fig.5, p.2126; orthogonality Eq.(26), p.2128	high (equation verified)	No	paper_004_injection_locking_part2, phase_vs_amplitude_noise
C12 The cross-coupled-inverter sense-amplifier paper is unrelated to ISF/phase noise; the only conceptual link is the cross-coupled-pair regeneration/positive-feedback mechanism shared with latches/LC.	[P5] (Hajimiri–Heald, ISCAS 1998)	high (clearly off-topic by title/abstract)	No	paper_005_sense_amplifier, paper_summary_table, build_report
C13 PPV/adjoint/Floquet is the rigorous mathematical foundation of the ISF, coming from the broader literature (Demir 2000 DOI 10.1109/81.847872, Kärtner 1990 DOI 10.1002/cta.4490180505), not among the 5 source PDFs; citation volume/issue/page/DOI have been checked.	external (not in the source folder)	high (sourcing statement)	✓ citation	effective_isf, equation_index, references

Claims consistent across papers (mutually corroborating, high confidence)

These claims are supported by more than one paper, or reappear in different papers in different forms, corroborating each other:

• C2 (phase persists / amplitude decays): [P1] argues from the limit cycle that "phase has no restoring force"; [P4] corroborates from the amplitude side with the APF and the amplitude decay function that "amplitude perturbations are pulled back". Same physics, two angles.
• C3 ↔ C6 ($\Gamma_{rms}^2/q_{max}^2$): the phase noise in [P1] Eq.(21) and the jitter proportionality constant $\kappa^2$ in [P2] share the same $\Gamma_{rms}^2/q_{max}^2$ ratio — phase noise and accumulated jitter are the same physics in the frequency and time domains.
• C4/C5 (symmetry suppresses $1/f^3$): [P1] derives it theoretically from Eq.(23)(24); [P2]'s Fig. 17 corroborates it by measurement (phase noise minimum at the symmetric control voltage). Theory + experiment.
• C1 (LTV) and C10 (injection): the same $\Gamma$ determines both noise→phase ([P1]) and injection→phase ([P3]); the LTV viewpoint runs through both papers.

Claims needing manual verification (flagged ⚠️)

For the claims below, the direction of the statement is trustworthy, but the exact constants/equation forms should still be compared against the original PDFs; wherever they are used, this site retains a TODO: marker:

• C7: "ring phase noise independent of $N$" holds under fixed power, fixed frequency and a specific noise model; verified against [P2] Sec. V, Eq.(23)/(25), p.796. The FOM prefactor is $\frac{8}{3\eta}\,\frac{V_{DD}}{V_{char}}\,\frac{kT}{P}$ ($\eta$ is the stage-delay proportionality constant of Eq.(14), $\approx1$; $\gamma$ enters only through $V_{char}=\Delta V/\gamma$). The only item still needing verbatim confirmation is this prefactor itself; the $N$-independence conclusion is firmly verified.
• C8: [P2] Eq.(16), p.794 (v7 re-verified: the radical covers only the constant, $\Gamma_{rms}\propto N^{-3/2}$; confirmed by triple evidence — the text's $4/N^{1.5}$@$\eta=0.75$ and App.B Eq.(55). v3 had misread it as $N^{-3/4}$). The closed form is $\Gamma_{rms}=\sqrt{\dfrac{2\pi^2}{3\eta^3}}\;\dfrac{1}{N^{1.5}}$ (at $\eta=0.75$, $\approx 4/N^{1.5}$, the solid line in [P2] Fig.8).
• C10: the generalized Adler equation is verified against [P3]: the time-averaged form $d\theta/dt=\omega_0-\omega_{inj}+\frac{1}{T_{inj}}\int\tilde\Gamma(\omega_{inj}t+\theta)\,i_{inj}\,dt$ = Eq.(30), p.2113 (the original uses a plus sign), lock range $\omega_L=\tfrac12 I_{inj}\vert\tilde\Gamma_1\vert$ = Eq.(35), p.2114. (If some pages on this site write a minus sign in front of the averaged term, that is because this site's $\Gamma$ uses the opposite sign convention to [P3]; numerically equivalent.)
• C11: the APF is verified against [P4]: decomposition $D(\tau,\phi)=\tilde\Lambda(\phi)\,d(\tau,\phi)$ = Eq.(18), definition $\Delta(\phi):=\int_0^\infty D\,d\tau$ (units $\mathrm{A^{-1}}$) = Eq.(19), both on p.2126; ISF/APF orthogonality in an ideal LC = Eq.(26), p.2128.
• C13: this is the sourcing statement itself — the point is to honestly flag PPV/adjoint/Floquet as external literature, not among the 5 source PDFs; the citation volume/issue/page/DOI have been checked online (see references [E2]–[E4]).

Confidence vs Verify — the difference: high (equation verified) (e.g. C3, C5, and the verbatim-verified C7/C8/C10/C11 from v3) means the equation's LaTeX has been checked against the rendered pages and the original PDFs. C13's ✓ citation is a reminder to "verify external citations yourself" — it does not mean the site's statement is wrong.

Key takeaways

• All 13 teaching claims are filed against their source papers and confidence levels; C1–C12 are high confidence (C7/C8/C10/C11 verified verbatim in v3), only C13 carries ✓ citation (external literature — verify yourself).
• Cross-paper agreement: C2 ([P1]+[P4]), C3↔C6 ([P1]+[P2] same ratio), C4/C5 ([P1] theory + [P2] measurement).
• Verified verbatim: ring constants (C7/C8, [P2] Eq.(16)/(23)), injection/APF forms (C10 [P3] Eq.(30)/(35), C11 [P4] Eq.(18)/(19)/(26)); external-literature sourcing (C13) is verify-yourself.
• PPV/adjoint/Floquet (C13) is not among the 5 source PDFs — external literature, honestly flagged.

Further reading

• Paper roles and the "no dedicated PPV/PSS paper" note: paper_summary_table
• Equation → derivation page → source: equation_index
• Source and toy flags for every figure: figure_index
• External literature (Demir, Leeson, Adler): references